Variable-angle gears

ABSTRACT

A pair of distinctive spherical gears transmits rotary motion between two shafts, while allowing the angle between the shafts to vary (e.g., by even more than 40°) continuously during operation. The term &#34;spherical&#34; is used to distinguish these distinctive gears from conventional &#34;cylindrical&#34; (spur and helical) and &#34;conical&#34; (bevel and hypoid) gears. Several forms of spherical gear teeth are specifically detailed and applied in designs appropriate for automotive constant-velocity joints.

TECHNICAL FIELD

The invention relates to gearing and, more particularly, to gear systemsfor directly connecting two shafts in a manner that transmits rotationfrom the driving shaft to the driven shaft while, at the same time,permitting the angle of intersection between the axes of the shafts tobe varied away from 180°-alignment over a relatively wide and continuousrange of angles (e.g., ±40°).

BACKGROUND OF INVENTION

For centuries, external and internal cog wheels and spur gears have beenused to interconnect shafts on aligned and parallel axes, while bevelgears have been used to transmit rotational forces between shafts havingaxes that intersect with each other at fixed angles extending over thefull range from 90° to 180°. During this century, hypoid gears have beendeveloped to accomplish the same purpose with shafts that not onlyintersect with each other over the full range of wide angles but whoseaxes are offset (i.e., non-intersecting). For such known internal andexternal spur gearing, shaft alignment is an absolute necessity; andknown bevel and hypoid gear pairs are designed specifically for only onepredetermined angle between the axes of the gears.

There are, however, some known special coupling and joint arrangementsfor compensating for small shaft misalignments where forces are beingtransmitted between aligned axes that must experience small angularchanges during operation. For instance, it is known to usedouble-crowned spur gears in nylon sleeves for coupling shafts that mayexperience slight relative movements in parallel offset (e.g., 0.040"/1mm) or slight angular misalignment (e.g., <1°). However, for eachsignificant degree of angular change (e.g., >1°) between the axes, acompletely new set of mating gears must be designed and manufactured toassure proper coupling and transmission of the rotational forces.

Of course, there are known non-gear means for transmitting rotary motionbetween shafts experiencing angular change. Perhaps the best known ofsuch devices are the universal joints used to connect the drive shaftsand wheel axles of automotive vehicles. Such universal joints are oftenconstructed in the form of two small intersecting axles, each held by arespective yoke. However, the shafts connected by such yoke and axlejoints do not turn at the same rate of rotation throughout each entirerevolution. Therefore, constant-velocity ("CV") joints have beendeveloped (e.g., Rzeppa and Birfield) in which the points of connectionbetween the angled shafts are provided by rolling balls which, duringeach revolution of the driving and driven shafts, roll back and forth inindividual tracks to maintain their respective centers at all times in aplane which bisects the instantaneous angle formed between the shafts.

Such universal and CV joints are quite complex and relatively difficultto lubricate, and the design and manufacture of such joint components iswidely recognized as a very specialized and esoteric art of criticalimportance to the worldwide automotive industry. While this CV joint artis very well developed, the joints are expensive, comprising many partsthat are difficult to manufacture; and such joints are limited in regardto the rotational speeds that they can transmit and in regard to theangles over which they can operate. Further, the rotational speeds thatcan be achieved by such joints are limited by the inertia of the rollingballs whose motion must reverse during each revolution.

Our invention has broad potential utility in any technology in whichmotion is transmitted between axes that intersect at variable anglesduring operation; and, as shown in specific embodiments disclosed below,our invention has particular applicability to, and provides remarkableimprovements in, the CV joint art, providing the basis for remarkablysimplifying and improving the design of CV joints.

SUMMARY OF THE INVENTION

In its broadest sense, the invention is a gear system with novel formsof gearing for directly connecting two shafts in a manner that transmitsrotation from the driving shaft to the driven shaft while, at the sametime, permitting the angle of intersection between the axes of theshafts ("shaft angle") to be varied. Such angular variation is possibleover a wide and continuous range extending to each side of 180° (i.e.,extending to each side of the position where the axes are either inparallel alignment or are coincident) to some preferred maximum anglediffering from 180° by more than 2° (e.g., 40°). As used herein, theterm "preferred maximum angle" indicates any angle (differing from 180°in either direction) up to which the shafts must be able to intersectfor the satisfactory transmission of rotational forces in the particularapplication in which the gear system is being used. For instance, if thepreferred maximum angle were 40°, possible articulation would be up to40° on each side of the 180° alignment position; and this would allowthe shafts, while they were transmitting rotational forces, to beangularly adjusted relative to each other over a full range of 80°.

Basically, the invention uses a single pair of gears to transmitconstant velocity between two shafts, while allowing the angle betweenthe shafts to vary during operation. In the most preferred embodiment,the shaft axes can be articulated relative to each other about a commonpivot point in any plane; and this is accomplished by a design in whichthe pitch circles of the two gears are of identical size and alwaysremain, in effect, as great circles on the same pitch sphere. As isaxiomatic in spherical geometry, such great circles intersect at twopoints, and the pair of lunes formed on the surface of the spherebetween the intersecting great circles (i.e., between the pitch circlesof the gears) inscribe a giant lemniscate ("figure-eight") around thesurface of the sphere. We believe that, since the relative movement ofthe tooth contact points shared between the mating gears inscriberespective lemniscates at all relative angular adjustments of the gearshafts, the two shafts rotate at constant velocity.

As has just been indicated, in the explanation below relating to thedesign and manufacture of the gears, the pitch circles of each gear canbe considered theoretically to be great circles on the same pitchsphere. However, each gear of the pair must of course have its ownrespective theoretical pitch surface (in order to account for relativemotion between the gears), so each gear should also be thought oftheoretically as having its own respective pitch surface in the form ofa respective one of a pair of respective pitch spheres which havecoincident centers and radii which are substantially identical but whichpermit each pitch sphere to rotate about its respective axis. Therefore,each pitch circle can also be considered theoretically to be,respectively, a great circle on a respective one of these substantiallyidentical pitch spheres so that the pitch circles of the gear paireffectively intersect with each other at two points separated by 180°(i.e., "poles"), and the axes of rotation of the two respective pitchspheres intersect at the coincident centers of the two pitch spheres atall times and at all angles of intersection.

For this primary organization of the invention, we use a first gear withinternal teeth having a predetermined pitch circle, and then mate itwith a second gear with external teeth and having a pitch circleidentical to the first gear. The gears have mating teeth that are inmesh at two areas centered 180° apart; and, since their pitch circlesare the same size, they rotate at a 1:1 ratio.

The invention can also be organized to transmit rotary motion at a 1:1ratio using two external gears, or to transmit rotary motion at ratiosother than 1:1. In disclosed embodiments of this latter type oforganization, the effective pitch circles of the gears are each,respectively, a great circle on a respective one of twodifferently-sized spheres that share one point of tangency, the smallerof the two spheres being positioned either inside or outside the largersphere. However, in these embodiments, the gears share only a singlemeshing area in a manner similar to conventional internal or externalgearing arrangements; and, of course, the axes of the gears are inparallel planes so that the variable angles of intersection between theaxes are measured by projecting one plane upon the other.

For use with either of these just-described organizations of thevariable-angle gear system, four different gear tooth designs aredisclosed, namely: a circle/tangent ("CT") design, a circle-on-diamond("CD") design, a "lune" design, and a lune/inverse-curve ("L/IC")design, all of which are described in detail below. All of these designspermit the axes of the gears to variably intersect throughout a range ofangles measuring from each side of 180° up to some preferred maximumangle, and all share a common feature: At least the central portion ofthe lengthwise tooth surface of each mating tooth, when viewed on apitch surface of its gear, is an arc of a single circle with a diameterselected so that, when said gears are rotating in a driving and drivenrelationship, the intersecting axes can be varied continuouslythroughout this preferred range of angles. [NOTE: For each of our gears,its respective "pitch surface" is a pitch sphere.]

In the CT and CD designs (and in one gear of the pair in the L/ICcombination), only the central portion of each tooth, when viewed in thepitch plane, is formed with the arc of a single circle; while in thelune design, the entire lengthwise curvature of each tooth surface isthe arc of a single circle.

In the preferred designs for our gears, a diametral pitch is selected sothat, when the axes of the gears are inclined to each other at themaximum preferred angle, two or more of the mating teeth of each gearwill be in mesh simultaneously at the each of the meshing areas sharedbetween the gears. As in conventional gearing design, tooth thickness isselected to assure that expected loads will be safely transmitted by thenumber of teeth in mesh.

In the CT and CD designs, the central portions of both tooth surfaces ofeach mating tooth, when viewed in a pitch plane, are respective arcsthat form the opposite sides of a single circle of predetermineddiameter.

In the lune design, the arc that forms the entire lengthwise curvatureof each tooth surface is also taken from a single circle ofpredetermined diameter. However, in the lune design, the circle isidentical to a particular circle formed on the surface of a particularsphere, and its diameter subtends an angle, measured from the center ofthe sphere, equal to the maximum desired angle of intersection betweenthe gear axes. The lune design for 1:1 arrangements is a circle formedon the sphere on which the pitch circles of each gear are great circles;and for arrangements other than 1:1, the circle is formed on the largerof the two intersecting spheres.

The CT, CD, and L/IC designs are preferred for embodiments in which thegears may drive and be driven in either direction, since the CT, CD, andL/IC teeth operate satisfactorily with no backlash (i.e., with onlyminimal assembly tolerance). In contrast, the lune teeth mesh withoutbacklash only when the axes of the gears intersect at the maximumdesired angle. The backlash between the lune teeth increases to amaximum when the shaft axes are aligned at 180°. Therefore, the lunedesign is not practical where large backlash would create operatingproblems.

For 1:1 arrangements, the teeth of the gears can be made withstraight-sided profiles between top and bottom lands, because (a) themating teeth do not "roll" relative to each other but rather, in amanner somewhat similar to hypoid gears, share sliding contact, and (b)the straight tooth sides lengthen the contact pattern on the matingteeth. Further, as will be apparent from the detailed description below,an involute profile would be relatively incompatible with the CT, CD,and L/IC designs.

However, involute profile is quite compatible with the lune design, andsuch involute profile is necessary for arrangements other than 1:1,because the teeth must roll together as well as slide past each other.In addition, the involute profile may be desirable in certain 1:1arrangements in which the gears do not transmit rotational motion butonly nutate.

The basic tooth designs of the invention are disclosed in detail alongwith various applications of the invention in novel CV-joint structureswith features that combine a wide range of angular articulation in allplanes with remarkable reductions in size and weight as well as ease oflubrication.

DRAWINGS

FIG. 1 is a schematic and partially cross-sectional view of a pair ofgears according to a first arrangement of the invention for transmittingrotational forces at a 1:1 ratio between a pair of shafts aligned onvariably-intersecting axes, the gears being mounted within respectivesupport frames and the respective shafts shown with their axes in 180°alignment.

FIG. 2 is a symbolic partial view representing just the gear and shaftportions of the gear system of FIG. 1, but showing the axes of the gearsintersecting at a preferred maximum angle.

FIGS. 3A, 3B, and 3C illustrate schematically the relative motionbetween sets of tooth contact points on the pitch surfaces of a pair ofrotating mating gears arranged in the manner generally indicated in FIG.2.

FIG. 4 is a graphic-type representation of the relative motion betweenone of the respective sets of tooth contact points illustrated in FIGS.3A, 3B, and 3C.

FIG. 5A is a schematic representation of a portion of the pair of matinggears of FIG. 1, showing the gears with their respective axes aligned at180° and indicating the projected chordal center distance betweensuccessive teeth on the pitch circle of each gear; and FIG. 5B is aschematic representation of a portion of the same pair of gears variablyintersecting (as in FIG. 3) at a selected maximum preferred angle x,showing their meshing teeth in a modified flat projection as the gearsrotate about their respective axes.

FIG. 6 is a schematic representation of the partial outline of themeshing teeth of a pair of gears according to the invention taken in theradial center plane of the gears with axes aligned at 180°.

FIG. 7 is a schematic representation of the outline of a gear toothaccording to the invention's CT design, the outline being shown in apitch plane of its gear.

FIGS. 8A, 8B, and 8C are schematic representations of the outlines ofthe meshing teeth of a pair of gears according to the invention's CTdesign, the outlines being shown in modified flat projections, and thepair being shown with their axes intersecting at the preferred maximumangle x; FIG. 8A represents a first one of the gear pair's meshingareas, while FIG. 8B shows the second meshing area at the same instantin time; and FIG. 8C represents the second meshing area shown in FIG. 8Bafter the gears have each rotated a further distance of three-quartersof the circular pitch.

FIGS. 9A and 9B show geometric constructions for determining the toothshape of a pair of gears according to the invention's CD design.

FIG. 10 is a schematic representation of the outlines of the meshingteeth of a pair of gears according to the invention's CD design, theoutlines being shown in modified flat projections.

FIG. 11 is a schematic representation of the meshing teeth of a furtherpair of gears according to a further shape variation that is applicableto either the invention's CT or CD designs, the meshing teeth beingshown in outline in modified flat projections.

FIG. 12 is a schematic representation of the very slight tip reliefclearance required on CD and CT design teeth, the tip relief being showngreatly exaggerated in the the illustration.

FIGS. 13A and 13B are schematic representations of gear teeth shapedaccording to the invention's "lune" design, FIG. 13A showing thegeometric construction for determining the circular arc that forms thelengthwise curvature of each tooth face, and FIG. 13B showing two setsof meshing teeth as the gears rotate about respective axes variablyintersecting at a selected maximum angle, the outlines of the gear teethagain being shown in modified flat projections.

FIGS. 14A and 14B are schematic representations of the outlines of themeshing teeth of a pair of gears according to the invention's L/ICdesign, the outlines being shown in modified flat projections of thepair; in FIG. 14A the axes of the gears are intersecting at a preferredmaximum angle, while in FIG. 14B the axes are intersecting at 20°.

FIG. 15 is a schematic and partially cross-sectional view of a firstembodiment of a constant-velocity joint according to the invention.

FIG. 16 is a schematic and partially cross-sectional view of anotherembodiment of a constant-velocity joint according to the invention, thisembodiment being preferred for use under high speed and high torqueconditions.

FIG. 17 is a schematic representation of two constant-velocity joints,similar to that shown in FIG. 15, incorporated in an articulated driveshaft assembly.

FIG. 18 is a schematic representation of a constant-velocity joint,similar to that shown in FIG. 15, incorporated in a steered drive-axlefor a vehicle.

FIG. 19 is a schematic and partially cross-sectional representation of arotating constant-velocity joint similar to that shown in FIG. 15, thejoint being articulated in the plane of the paper and including anencapsulating boot and lubricating fluid.

FIGS. 20A and 20B are schematic representations of two views of afurther embodiment of the inventive gear system in an arrangement fortransmitting rotational forces at a ratio other than 1:1, FIG. 20Ashowing a top view of an internal/external gear pair supported on shaftsintersecting at an angle less that 180°, and FIG. 20B showing an endview of only the gears of the same pair when their respective shafts arealigned at 180°.

FIG. 21 is a schematic representation of still another arrangement ofthe inventive gear system for transmitting rotational forces at ratiosother than 1:1, this embodiment using only external gearing.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Gear System

FIGS. 1 through 5B illustrate various features of a pair of gears in afirst arrangement of the invention for interconnecting a pair ofrotating shafts. In FIG. 1, which is a schematic and partiallycross-sectional view of this first arrangement, an internal gear 10fixed to a cup-like support 12 is splined to a shaft 14 held in ajournal 16 of a carrier 26. A mating external gear 20 is fixed forrotation to the hub 22 of a second shaft 24, the latter being supportedin a housing 18 for rotation in an appropriate bearing 28. Carrier 26 isitself pivotally mounted to housing 18 by pins 30 for rotation aboutaxis 32.

In FIG. 1, shafts 14 and 24 are shown with their respective axes 40, 42positioned in 180° alignment. (A portion of the teeth of gears 10 and 20are shown in this 180° alignment in FIG. 5A.) In this position, theteeth of gears 10 and 20 mesh together in the same manner as the teethof a geared coupling.

A spherical bearing, comprising interior member 34 and exterior member36, maintains the mating gears 10 and 20 in proper meshing relationship.Namely, interior member 34 is bolted to the end of shaft 14, whileexterior member 36 is captured between hub 22 and a lip 38 on theinterior of gear 20.

FIG. 2 represents, symbolically, just the gear and shaft portions of thegear system shown in FIG. 1. However, in FIG. 2 the axes 40, 42 ofshafts 14 and 24, respectively, are shown intersecting at a "preferredmaximum angle" (i.e., at some predetermined maximum shaft angle x up towhich the shaft axes may variably intersect while rotational forces arebeing transmitted).

Gear 20 is shown in solid lines pivoted about axis 32 at an angle x in afirst direction, and it is shown in phantom lines pivoted about axis 32at an angle x in the opposite direction. This illustrates the wideangular range of intersection through which the gear pair may bevariably pivoted while rotational forces are being satisfactorilytransmitted. At all times during such variable angular relative motionbetween the shaft axes, gears 10 and 20 remain in mesh at two respectivemeshing areas, the center of each meshing area being located at one ofthe two respective points at which the gears' respective pitch circlesintersect with axis 32.

In this basic first arrangement shown in FIGS. 1 through 5B, our gears10, 20 function in a manner similar to known gear couplings in that theydo not rotate relative to each other as their respective shafts rotateat a 1:1 ratio. However, whenever the angular orientation of theirrespective shafts is variably adjusted out of 180° alignment (as shownin FIG. 2), the teeth of the gears continuously move into and out ofmesh even though the gears rotate at all times at the same speed.

This relative movement of the teeth of gears 10, 20, into and out ofmesh, is shown schematically in FIGS. 3A, 3B, and 3C which represent,respectively, three different positions of relative gear rotation aboutaxes 40, 42 when axes 40, 42 are intersecting at some preferred maximumangle x. FIGS. 3A, 3B, and 3C show the relative advancement of fourdifferent respective sets of tooth contact points as the mating gearteeth move into and out of mesh.

In FIG. 3A, a tooth contact point A on internal gear 10 is in mesh withtooth contact point A' on external gear 20; and, simultaneously, a toothcontact point C on internal gear 10 is in mesh with a tooth contactpoint C' on external gear 20. FIG. 3B shows the same tooth contactpoints on each gear after the gears have rotated at 1:1 for a quarter ofa rotation, the gear tooth contact points D and B of gear 10 and pointsD' and B' of gear 20 now being in meshing contact. Following a furtherquarter turn, as shown in FIG. 3C, tooth contact points A, A' and C, C'are once again at mesh, but at a relative position 180° from theirinitial contact position shown in FIG. 3A.

The tooth contact points represented in FIGS. 3A, 3B, and 3C are alllocated on the pitch circles of their respective gears; and,geometrically, these pitch circles are each great circles on the samesphere. All great circles intersect each other at two positions 180°apart. FIG. 4 is a schematic representation of the relative motionbetween one of the respective sets of tooth contact points illustratedin FIGS. 3A, 3B, and 3C, namely, tracing the movement of tooth contactpoints A, A' along their respective pitch circles 10', 20' as gears 10,20 make one full revolution together. Although the respective pitchcircles are shown in flat projection, it can be seen that each toothcontact point traces a lemniscate-like pattern (a "figure-eight on thesurface of a sphere"); and, as is well known in the universal joint art,such lemniscate motion is essential when transferring constant velocitybetween two articulated shafts.

As indicated above, FIG. 5A schematically represents a portion of thepair of mating gears of FIG. 1, showing internal gear 10 and externalgear 20 with their respective axes aligned at 180°. In this position,respective pitch circles 10' and 20' are coincident. Indicated on thecoincident pitch circles are tooth centers 44 and 45 of internal gearteeth I₁ and I₂, respectively, and tooth centers 46, 47, and 48 ofexternal gear teeth E₁, E₂, and E₃, respectively. Also shown are theprojected chordal center distances PC between successive tooth centers46, 47 and tooth centers 47, 48.

FIG. 5B schematically represents approximately the same portion of gears10, 20 as shown in FIG. 5A. However, in FIG. 5B, the gears are shownvariably intersecting (as in FIG. 2) at selected maximum preferred anglex, and the gear teeth are represented in modified unwound flatprojections of the pitch spheres of each respective set of gear teeth.The flat projections are modified so that the center distance betweensuccessive teeth on each flat projection equals the projected chordaldistance PC between tooth centers.

NOTE: With reference to the flat projections and plane geometricconstructions used to illustrate our tooth forms, it must remembered ourgear system is based upon spherical geometry. That is, the projectionsonto the flat surfaces of our drawings represent lines on the surface ofthe respective sphere on which the pitch circle of the gear is a greatcircle. For instance, referring to the representation of theinternal/external gear combination in FIG. 5B, the flattened projectionsof the teeth of gears 10 and 20 can be theoretically considered to beeither on the surface of the same pitch sphere or, as indicated above,on the respective surfaces of one of a pair of respective pitch sphereshaving substantially equivalent radii and coincident centers.

As can be seen in FIG. 5B, when gears 10, 20 are rotating together withtheir respective axes variably intersecting at the preselected preferredmaximum angle x, the center of their meshing engagement is coincidentwith axis 32 about which the gears pivot relative to each other, and theload being transferred between the gears is shared by ten teeth. Thatis, while only five teeth are shown in meshing engagement in FIG. 5B, asexplained above (and as can be seen in FIG. 1), gears 10, 20 aresimultaneously in mesh at all times about two meshing centers located180° apart.

Special attention is called again to the fact that gears 10, 20 do notroll relative to each other in the manner that mating spur and helicalgears do in conventional gearing systems, and conventionally-designedgear teeth are not appropriate for our novel variable-angle gearingsystem for which we have developed unique gear tooth designs.

Gear Tooth Designs

(a) Basic Design Elements

As indicated above, the variable-angle gearing system can be used fortransmitting rotational forces at ratios other than 1:1. However, one ofits primary applications relates to such 1:1 arrangements, and thefollowing discussion is directed to the design of gear teeth appropriatefor such arrangements.

Referring to FIG. 6, the partial outline of the meshing teeth of a pairof gears 50, 52 according to the invention is represented schematically;and, for clarity, external gear 52 is not shown in cross section. Theaxes of the gears are aligned at 180°, and the outline is taken in theradial center plane of the gears. Two external gear teeth 54, 55 areshown in full mesh with three internal gear teeth 56, 57, 58.

As can be seen in FIG. 6, the working surfaces of all the gear teeth arestraight-sided. This is the preferred profile shape. As just explainedabove, whenever the axes of our gears are positioned out of the 180°alignment while the gears are rotating at a 1:1 ratio, the gears areconstantly moving into and out of mesh about their two shared meshingcenters. This movement causes the surfaces of the meshing teeth to slideover each other in a manner somewhat similar to the sliding contact thatoccurs between the meshing teeth of hypoid gears. The preferredstraight-sided tooth surfaces create a full line of sliding contactthrough the mesh. Further, while the straight-sided teeth can bedesigned to follow radial lines 60, a spline shape (indicated by lines62) is preferred.

There is another characteristic common to gear teeth according to ourinvention, and this will be illustrated by using as an example a geartooth formed according to the invention's CT (circle-tangent) design.FIG. 7 is a schematic representation of the outline of a CT gear tooth64, the outline being shown in a pitch plane of its gear. This CT tooth,like all teeth according to our invention, includes the following basicdesign characteristic: The central portions 66, 67 of the workingsurfaces of tooth 64, on each side of its radial center line 68, areformed by the arc of a single circle 70 having a diameter selected sothat, when its gear is rotating in a driving and driven relationshipwith a mating gear according to our invention, the intersection of theaxes of the mating gears can be varied continuously from an alignment of180° throughout the range of angles extending to some preselectedmaximum preferred angle on each side of 180°. The circular arcs thatform the central portions of the two working faces of each CT and CDtooth (and one of the teeth of the combination L/IC design) are formedfrom the same circle; however, while the two working faces of each lunetooth are also arcs of circles having the same diameter, they are notformed on the same circle. These features are discussed in greaterdetail below.

In addition, the diameter for the required single circle in all of ourdesigns is selected to assure that more than two mating teeth shall bein mesh simultaneously about each of the meshing centers shared by themating gears. The selection of the diameter of the single circle will bedescribed, along with other parameters, in the following explanations offour preferred tooth designs for our invention.

(b) CT (Circle-Tangent) Tooth Design

As just explained above and as can be seen in FIG. 7, the design of theCT gear teeth begins with the selection of a single circle. This firststep is approached in the same manner as is well known in the gearingart, namely, size and strength specifications for our gear pair areinitially determined in accordance with the application in which ourvariable-angle gear system is to be used (e.g., as a CV joint for asteer/drive axle in an automotive light truck). The addendum circle(maximum diameter) of the gears may be limited by the physical space inwhich the gearing must operate, and a diametral pitch must be selectedso that the normal chordal thickness of the teeth (i.e., the chordalthickness of each tooth along the pitch circle) is sufficient to permitthe maximum expected load to be carried by the number of teeth in mesh.

In this regard, it is essential to remember that when using the gearsystem for transferring motion at a 1:1 ratio, a pair of our gears iscapable of handling twice the load as a pair of conventional gears ofthe same size. That is, since the gear pairs share two meshing areascentered 180° apart, they have twice as many teeth in mesh as would aconventional gear of the same size, and a diametral pitch may beselected that provides a normal chordal thickness that is significantlysmaller than would be conventionally required.

Referring again to FIG. 7, following the selection of an appropriateaddendum size and diametral pitch, a single circle 70 is used to formthe central portion of the tooth. Circle 70 has a radius R whichproduces a circle having the required normal chordal thickness D alongradial center line 68.

Next, it is preferred to extend the lengthwise face width of each gearsufficiently to assure that more than two teeth will be in mesh abouteach of the two meshing centers shared by our gear pair. To accomplishthis, an initial determination is made regarding the angular variabilitythat will be required for the particular application. For instance: auniversal joint designed for a specific truck drive shaft may require nomore than 5°-10°, but even more than 40° of articulation may be neededin a steer-drive. As indicated above, we refer to this desired angularvariability as the "preferred maximum angle x".

In the example illustrated in FIG. 7, it is assumed that the preferredmaximum angle x is 40°. The angle x is marked off on each side of radialcenter line 68 (indicated by the construction lines between points ABand EF) so that points A and E measure respective tooth surface angles x(in this example, 40°) on each side of center line 68 on tooth surface66, and points F and B measure the same tooth surface angles on toothsurface 67.

Each respective tooth surface 66, 67 is then extended by constructingtooth surface extension portions outlined by straight lines 72, 73 and74, 75, respectively, each of which is drawn tangent to a respectivetooth surface angle point A, E, B, F. Each extension line 72, 73 and 74,75 is respectively extended from its point of tangency toward aprojected intersection with the axial center line 76, completing theconstruction of the tooth surface extension portions. In the final toothform, the sharp ends of these extension portions are preferablychamfered as indicated in dotted lines.

Since each extension line 72, 73 and 74, 75 is perpendicular to therespective radial line drawn to its point of tangency, it will be notedby simple geometric analysis that the angle formed between each saidextension line and axial center line 76 is also equal to x (in thisinstance, 40°).

Teeth proportioned according to this CT design will slide properly intoand out of mesh as our gears interconnect two shafts at variablyintersecting angles. Also, this CT design assures that, at one or bothof the gear pair's centers of meshing engagement, more than two matingteeth will carry the load even when the axes of the gears areintersecting at the maximum preferred angle.

Further, if the diametral pitch is selected so that each gear has an oddnumber of teeth, this design assures that more than two mating teethwill carry the load about both of the gear pair's centers of meshingengagement when the gears are intersecting at the maximum preferredangle. This latter condition is illustrated schematically in FIGS. 8Aand 8B which represent the outlines of the meshing teeth of a pair ofgears according to the invention's CT design, the outlines being shownin modified flat projections, and the pair being shown with their axesintersecting at the preferred maximum angle x.

FIG. 8A represents a first one of the meshing areas of a CT gear pairdesigned according to the method just described above, while FIG. 8Bshows the second meshing area of the same gear pair at the same instantin time. Once again, for purposes of illustration, it is assumed thatthe gear teeth have been designed for a preferred maximum angle of 40°.As indicated above, this provides an angular range that extends 40° toeach side of the position where the axes are either in parallelalignment or are coincident, thereby creating 80° of total articulation.

In FIG. 8A, the center of an external gear tooth 80 is positioned at thecenter of the first meshing area, and external gear tooth 80 is incontact with internal gear teeth 81, 82. At the same instant of time, atthe second shared meshing area shown in FIG. 8B, the center of aninternal gear tooth 83 is positioned at the center of the meshing area,and internal gear tooth 83 is in contact with external gear teeth 84,85. Thus, when the shafts being interconnected by the gear pair areintersecting at the maximum angle, six gear teeth are sharing the load.

FIG. 8C represents the second meshing area shown in FIG. 8B at a momentin time after the gears have each rotated a further distance ofthree-quarters of the circular pitch. At the time illustrated in FIG.8C, the radial center line of external gear tooth 86 has come intocontact with the right hand extension portion of internal gear tooth 87,and the line of contact between these two teeth begins its slidingmovement to the right (as viewed in the drawing) along the front face oftooth 86 and to the left along the rear face of tooth 87. At the sametime, the line of contact between internal gear tooth 87 and externalgear tooth 85 is sliding to the left along the front face of tooth 87and to the right along the rear face of tooth 85.

As just indicated above, the number of teeth in mesh when the shafts areoriented at the preferred maximum angle x represents the minimum numberof teeth in mesh for all expected operating conditions; and when theshafts move into substantial alignment at 180°, the teeth of the twogears are all fully meshed with each other in a coupling-like manner.Therefore, if the selected diametral pitch and normal chordal thicknessof the teeth are sufficient to carry expected loads with the number ofteeth in mesh at the preferred maximum angle, the gear pair will haveappropriate strength under lesser angular orientations.

Persons skilled in the gearing art will appreciate that the possiblescoring of the gear tooth faces must be given special consideration inview of the sliding contact between our gears. However, when consideringthe possibility of scoring in our gear system, it should be noted that(a) the surface pressure on each tooth is reduced, since the load isshared by multiple teeth at two meshes simultaneously, and (b) theopposite tooth faces of each tooth are under load, respectively, at eachof the shared meshes. Also, the tooth surface distance through whicheach pair of meshing teeth slide relative to each other, as they passinto and out of mesh, is reduced as the shaft angle approaches 180°.Therefore, the sliding velocity decreases as the shaft angle between thegears decreases, and the potential for scoring problems should beminimized if the surface pressure and the sliding velocity between thegear teeth are acceptable at the preferred maximum angle.

(c) Design of CD (Circle-Over-Diamond) Teeth

While there may be other ways to determine the design parameters of gearteeth appropriate for our variable-angle gear system, we have done thisby general geometric construction; and the general geometricconstruction for our CD teeth, illustrated in FIGS. 9A and 9B, is asfollows:

(1) In the same manner as was explained above in regard to the CT teeth,the design of the CD teeth also begins by initially determining requiredsize and strength specifications in accordance with the application inwhich the gearing is to be used and, therefrom, selecting an appropriateaddendum size, diametral pitch, and normal chordal thickness for theteeth.

(2) Following the initial selection of such appropriate basicparameters, a portion of the external gear of the pair is laid out in anaxial view in the manner shown in the right hand portion of FIG. 9A.Namely, a portion of its pitch circle a and at least two tooth centers band c are constructed. A radial line d passing through a tooth center bis selected to mark off the center of a "proposed mesh", and an unwoundflat projection a' of a portion of the pitch circle a of the externalgear is laid out perpendicular to radial line d.

(3) A projected tooth center b' is marked at the intersection of radialline d and unwound pitch circle a' to serve, as indicated above, as thecenter of the proposed mesh. Then, a second tooth center c, adjacent totooth center b, is projected from originally constructed pitch circle ato unwound pitch circle a', being identified as projected tooth centerc'.

(4) Next, circles e and f are constructed about tooth centers b' and c',respectively, each circle having a diameter equal to the normal chordaltooth thickness determined by the diametral pitch selected in step (1)above. As those skilled in the art will appreciate, this diameter isalso equal to one-half of the projected circular pitch of the gear (asindicated by the dotted circle of the same diameter shown midway betweenprojected tooth centers b' and c').

(5) The unwound flat projection of the pitch circle g of the internalgear of the pair is then drawn through the center b' of the proposedmesh at an angle x which is selected to be equal to the maximum desiredangle of intersection between the gear axes, and two new tooth centers hand i are marked on unwound pitch circle g, tooth centers h and i beingpositioned apart at a distance equal to the projected circular pitch andbeing centered about mesh center b'. New circles k and m, each havingthe same diameter as tooth circles e and f are drawn about centers h andi.

(6) Reference is now made to FIG. 9B which is a continuation of theprojected mesh construction begun in the left hand portion of FIG. 9A.Unwound pitch circle g also represents the radial center line of eachtooth circle k and m, and the angle x (which equals the preferredmaximum angle of intersection between the gear axes) is marked off oneach side of center line g on each of the opposite faces of tooth circlek, thereby creating two respective tooth face angles (of x°) on eachopposite face of tooth circle k. A chord n is then drawn between theouter points o and p of the respective tooth face angles on one side oftooth circle k, and a bisector q is constructed through tooth center hand chord n.

(7) A line is drawn from point o tangent to the surface of tooth circlef at r and ending at its intersection with bisector q at s. A secondline is drawn from point s to point p at the other end of chord a, andthe equal sides of the resulting isosceles triangle ops form the basicshape of an extension portion that increases the lengthwise width of thegear tooth in an axial direction on one side of tooth circle k. Thebisector q is now extended to form the axial center line of the tooth,and a triangle of identical dimensions is then drawn extending from theouter points of the respective tooth face angles on the opposite side oftooth circle k as shown in FIG. 9B, completing an extension portion inthe opposite axial direction.

(8) The outline of this apparent "circle-over-diamond" tooth shape, asconstructed about tooth center k in the manner just described, is thenused for the shape of the teeth (when viewed in a pitch plane of thegear) of both gears in a mating CD pair. Of course, as appreciated bythose skilled in the art of gear design and manufacture, while our finalCD tooth shape is substantially in this form, minor modifications mustbe made for tip-relief, clearance, edge and surface smoothing, etc.

A set of such meshing CD teeth are illustrated schematically in FIG. 10with the gears positioned about a center of mesh 88 and with the axes ofthe gears oriented at a selected preferred maximum angle of intersectionof 40°. At this maximum angle, it can be seen that three internal gearteeth 90, 91, 92 are in contact with two external gear teeth 93, 94.Therefore, like our other tooth designs, more CD teeth are in mesh atall times to carry expected loads than would be true with conventionalgear systems.

(d) Possible CT and CD Tooth Design Variation

FIG. 11 schematically represents the meshing teeth of a further pair ofgears according to a further shape variation that is applicable toeither the invention's CT or CD designs. Once again, the meshing teethare shown in outline in flat projections as the gears rotate aboutrespective axes variably intersecting at a selected preferred maximumangle, and the flat projections are modified in the same manner as wasnoted above in regard to FIG. 5B.

In this unusual variation, the respective gears of the mating pair haveteeth of different thickness. Once again, the design is by constructionand, in the initial design step, a diametral pitch is selected toprovide a tooth of minimum size and normal chordal thickness, but stillappropriate to carry expected loads. For instance, in FIG. 11 a portionof the CT teeth of an internal gear 100 are laid out in projection asshown; and by way of example, it can be assumed that internal gear 100has a pitch circle of about 9 cm (3.5") and is initially selected to bea 10-pitch/36-tooth gear with a normal chordal thickness as indicated inthe single circle 102 forming the center of one of its CT teeth. Thecircular pitch for the teeth of internal gear 100 is indicated as cp.

Next, every other tooth is removed from gear 100 as indicated by dottedlines. This leaves a space between each tooth of gear 100 that is equalto three times the diameter of single circle 102, while the remaininginternal gear teeth 104, 105, 106 are on centers that are two times theinitially selected circular pitch (i.e., 2·cp). Nonetheless, internalgear teeth 104, 105, 106 retain their original dimensions and shape(e.g., as they would appear in a 10-pitch/36-tooth gear).

In the next step of this variation, the teeth of mating external gear108 are constructed on centers that are also separated by 2·cp. However,when using the CT construction as explained above, the single circle 110(that is used to form the central portion of each tooth) is providedwith a diameter which is equal to three times the diameter of singlecircle 102 used to form the central portion of the original teeth ofinternal gear 100.

When the meshing portions of gears 100, 108, constructed in the mannerjust described above, are laid out in projections as shown in FIG. 11with the axes of the gears intersecting at a selected preferred maximumangle x (for this example, x=40°), it can be seen that thedifferently-sized teeth can rotate together in a mating relationship.Further, based upon the gear size parameters suggested as an exampleabove for gears 100, 108 in FIG. 11, each of the two gears become, ineffect, a 5-pitch/18 tooth gear, but they retain the same circular pitchand the same shallower whole depth as the original 10-pitch/36-toothgear would have had.

It can also be seen in FIG. 11 that two of the oversized external gearteeth 111, 112 are in contact with two internal gear teeth 105, 106.Therefore, this variation provides at least four mating teeth for eachmesh, i.e., eight teeth in mesh at all times during normal operation.

Our CT, CD, and L/IC gears share another design feature, namely, allrequire a very slight tip relief for clearance. In FIG. 12, such tiprelief is shown, in greatly exaggerated form, in a schematicperspective: a tooth face of an external gear CD tooth 114 has the upperaddendum of each of its respective extension portions 116, 117 chamferedslightly, the depth of the chamfer increasing from zero, at the radialcenter line of the tooth, to a maximum at the outside edge of the toothface as it meets the axial center line of the tooth. To provide someappreciation for the amount of relief required: the teeth of an externalCD gear with an outside diameter of 10 cm (4") would requireapproximately 0.2 mm (0.008") maximum tip relief at their outer edges.

Such slight tip relief can be simply generated during the manufacture ofour gearing. For instance, in a process in which the gears are initiallyforged to a "rough-but-near-finished" shape, the forged rough gears canbe finished by CBN grinding with a finishing tool having the form of amating gear without any tip relief.

(e) Lune Tooth Design

The gear system includes still another gear tooth design that is easilymanufactured and has particular utility in some applications. Thisdesign is called "lune" because the the outline of the entire lengthwisesurface of each of the opposite working faces of each tooth is formed bythe arc of a single circle, and when viewed on the pitch surface of thegear, the outline of the two working faces of each tooth create alune-like shape. (Geometrically, a "lune" is the area bounded by twointersecting great circles on the surface of a sphere.) For thisexplanation of our lune design, reference will be made to FIGS. 13A and13B.

FIG. 13A shows the geometric construction used to determine the circulararc that forms the lengthwise curvature of each tooth face. First, inthe same manner as was explained above in regard to our CT and CD teeth,the design of our lune teeth also begins by initially determiningrequired size and strength specifications in accordance with theapplication in which the gearing is to be used and, therefrom, selectingan appropriate addendum size, diametral pitch, and normal chordalthickness for the teeth. With this information, a simple construction ismade of a radial cross section of the external gear 115, laying out theaddendum circle 116, the root circle 118, and the pitch circle 120; andthe outlines of a few teeth are also added.

Next, the preselected preferred maximum angle x (in this example: 25°)is laid out from the gear center 122 between radial lines 124, 125; anda chord 126 is drawn between the two respective points 127, 128 at whichradial lines 124, 125 intersect pitch circle 120. The length of chord126 is measured to provide the diameter measurement X which is used forcreating the single circle that determines the arc that forms the entirelength of the working surface of each lune tooth for the gears.

In a further construction shown in FIG. 13B, external gear 115 and amating internal gear 130 are laid out in modified flat projections (asexplained above) with the axes of the gears intersecting at thepreselected preferred maximum angle (i.e., 25°) , the pivot axis aboutwhich the gear axes intersect being indicated by the center 132 of theshared mesh. A circle having a diameter of X is drawn about center 132,and the arcs of this circle form the front face of external gear tooth134 and the rear face of external gear tooth 135. Center 132 is alsoused to mark the center of an external tooth, and further external toothcenters 137, 138 are marked off along radial center line 136 of gear 115at successive distances equal to the preselected circular pitch.Thereafter, using circles of the same diameter X and using thesuccessive centers 137, 138, etc., the front and rear faces of the otherexternal gear teeth are constructed.

Similarly, beginning at two points marked off at a distance of one-halfthe circular pitch on each side of mesh center 132, successive toothcenters 139, 140 are marked off along radial center line 141 of internalgear 130. Then, using circles of the same diameter X and using thesuccessive centers 139, 140, etc., the front and rear faces of the gearteeth of internal gear 130 are constructed. As will be readilyunderstood by persons skilled in the manufacture of gears, such lunegear teeth can be formed by using hollow cylindrical cutters with aninside diameter of X.

With this construction as shown, it can be seen that many lune teeth(e.g., approximately 10 teeth at each shared meshing area) will be infull contact on both of their respective faces when the shaft anglebetween the gears is at the maximum angle. However, the normal chordalthickness of each lune tooth is not as large as the space between theteeth of its mating gear so that, as the shaft angle decreases from thismaximum orientation back toward 180° alignment, the backlash between themeshing lune teeth increases, reaching a fairly substantial maximumamount of backlash when the axles reach 180° alignment. Therefore, ourlune-tooth design is not appropriate for applications in which minimumbacklash is required at all times, e.g., where expected shaft rotationreversals occur with relative frequency during normal operation.

(f) Combination Lune/Inverse Curve ("L/IC") Design

FIGS. 14A and 14B are schematic representations of the outlines of themeshing teeth of still another pair of gears according to the invention.For reasons that will be apparent from the following explanation, thisdesign is called a lune/inverse-curve combination ("L/IC"). Once again,the outlines of the teeth are shown in modified flat projections of thepair with their axes intersecting at a preferred maximum angle. Ofcourse, it must be remembered that such flat projection merely simulatesthe real gears whose pitch surfaces are spherical.

That is, should the gears illustrated in FIG. 14A be erroneously laidout in the traditional manner on pitch "cylinders", serious interferencewould occur. However, when laid out on a pitch sphere (or on respectiveones of a pair of respective pitch spheres having substantiallyequivalent radii and coincident centers), these teeth will meshthroughout the full range of angular adjustment without interference orexcessive backlash.

As with the other tooth designs just described above, the teeth shown inFIGS. 14A and 14B are most easily explained by means of a construction.For these L/IC teeth, a construction of the design begins with the usualinitial determination for selecting an appropriate addendum size,diametral pitch, and normal chordal thickness for the teeth, as well asthe desired maximum angle x through which the gear shafts shall beexpected to variably intersect to each side of 180°.

Based upon these preselected parameters, flat projections of the pitchcircles of the two gears are laid out intersecting at the maximum angle(in this case at an angle of 45°); and, as with the CT and CD designs, atooth center 80' for one of the gears is positioned at the point ofintersection between the pitch circles. Using the selected circularpitch P', additional tooth centers 81', 82', and 83', 84', 85' and 86',respectively, are marked on each pitch circle. Next, the central portionof each tooth is laid out as a respective circle having a diameterequivalent to the desired chordal thickness D'. Namely, each respectivecircle is made with a radius T that is equivalent to one-half thechordal thickness (i,e., one-quarter the circular pitch).

The teeth of a first one of the gears are then formed with a lunedesign, the entire length of each tooth face 87', 88', 89', 90' of eachtooth being the arc of a circle having its center located on the pitchcircle of the first gear and having a radius R' such that: ##EQU1##radius R' being equivalent to one and one-half times the selectedchordal thickness, which is also equivalent to three-quarters of thecircular pitch.

The teeth of the mating gear of the second gear are formed about toothcenters 80', 81', 82' in a manner quite similar to that described abovewith regard to our CT and CD teeth. Namely, each circular-arc centerportion 91', 92' of each tooth surface is provided with twoaxially-extending portions 93', 94' contiguous, respectively, with eachof its ends; and the surface of each respective extension portion 93',94' is a line (a) extending from circular central portion 91', 92' at arespective one of two points A', E' and B', F' oppositely disposed fromthe radial center line 95' of the tooth at respective predeterminedtooth surface angles x and (b) extending toward a projected intersectionwith the axial center line 96' of the tooth. Also, in our L/IC design,like our CT design, the surface of each respective tooth surfaceextension portion is tangent to the circular central portion of eachtooth face.

However, as can be seen in FIG. 14A, each respective tooth surfaceextension portion 93', 94' is a curved line having a curvature inverseto the curvature of circular central portion 91'. Each of theseinversely-curved extension portions is a circular arc with a center ofcurvature positioned on an extension of its respective tooth surfaceangle line A', B' and E', F'. Such a construction is shown for the toothsurface extension portions of tooth 97', for which the centers ofcurvature for extension portions 100', 101', 102' and 103' are,respectively, points 104', 105', 106' and 107'. In this construction,the radius R' of each extension portion is equivalent to three times theradius T of its respective circular central portion.

FIG. 14B illustrates the same mesh of the same pair of L/IC gears shownin FIG. 14A, but with their axes intersecting at only 20° rather than atthe preferred maximum angle. It can be seen that five teeth are still inmesh. Therefore, our L/IC design also provides more teeth in mesh at alltimes than does a conventional gear system; and, further, when the axesare aligned at 180°, all the teeth are in mesh as in a gear coupling.

Constant-Velocity Joints

While the gear system can be used in any application that requires thetransfer of rotational forces between elements whose axes intersect atvariable angles during normal operation, one of its primary applicationsis in automotive technology relating to universal and constant-velocity("CV") joints.

In FIG. 15, a first embodiment of a CV joint according to the inventionis shown in a schematic and partially cross-sectional view. One of ourexternal gears 150 is mounted to a hub 152 splined to the end of a driveshaft 154, and its mating internal gear 156 is mounted to a cup-likesupport 158 fixed to the end of a driven shaft 160. Gears 150 and 156are maintained in a meshing relationship by means of a spherical bearingcomprising a large ball bearing 162 fixed to the center of support 158at the end of driven shaft 160 by a bolt 163. Ball bearing 162 is heldin a cage 164 that is trapped between an outer lip 166 of hub 152 and aspring ring 168 located by an appropriate channel in hub 152.

For assembly purposes, the splined end of hub 152 is bored out all theway to the inside diameter of the splines, and cage 164 is divided intotwo parts. During assembly: (a) the outer half of cage 164 is placedagainst lip 166, (b) ball 162 is placed in the outer half of cage 164,(c) the inner half of cage 164 is positioned around ball 162, (d) springring 168 is positioned in hub 152 to retain cage 164, and (e) bolt 163is used to secure ball 162 to shaft 160.

With this bearing structure, the centers of both gears are maintained atall times coincident with the center of ball 162, while ball 162 is freeto move in any direction relative to its cage 164; and gears 150, 156remain in mating contact about two meshing centers as shafts 154, 160intersect variably throughout a wide range of shaft angles in any plane.

FIG. 16 is a schematic and partially cross-sectional view of anotherembodiment of a constant-velocity joint according to the invention.While this further embodiment is similar to the CV joint of FIG. 15, itincludes a special spherical bearing that is preferred for use underhigh speed and high torque conditions.

Internal gear 170 is fixed to cup-like support 172 and driven shaft 173,while external gear 175 is fixed to a hub structure 176 splined to driveshaft 177, and the central portion of the spherical bearing once againcomprises a large ball 178 secured to support 172 and shaft 173 by abolt 179. Also, ball 178 rides in a cage 180 that is retained in anappropriate channel formed in hub structure 176. However, in thisheavy-duty embodiment, ball 178 does not ride directly on cage 180 butrather is supported by many smaller balls 182 that are trapped in cage180 by a series of races formed by very thin ring washers 183 which arelatitudinally positioned about ball 178. For assembly purposes, cage 182is again split into two parts secured by bolts 184 (only one shown).With this ball-bearing arrangement, separate groups of smaller balls 182are each retained, respectively, in separate latitudinal raceways, butthe balls remain free to roll longitudinally.

In the manner explained above, the teeth of the gears used in these CVjoints are designed for some predetermined maximum preferred shaftangle. In FIG. 16, the CV joint is shown articulated in the plane of thepaper about pivot axis 186 to its preferred maximum angle (in thisexample: 40°); and, to illustrate the range of articulation of this CVjoint, the lower end of gear 175 is also shown in phantom lines,indicating the position of gear 175 when it is pivoted to the samemaximum angle in the opposite direction.

Lubrication of the spherical bearings of these CV joints is facilitatedby suitable channels bored through, and around the surface of, the largeballs (such channels are only shown in FIG. 15). Also in this regard,those skilled in the art will appreciate that during shaft anglechanges, e.g., caused by the rise and fall of a knee-action supporteddrive wheel, the hubs (e.g., hub 152 and hub structure 176) must moveslightly axially relative to the ends of their respective shafts. Underthese circumstances, lubricating fluid trapped between the end of shaft177 and ball 178 is pumped through and around the spherical bearing.

It should be noted that the ball-mounted CV joints just described aboveare capable of articulation in any plane passing through the center ofthe ball. Of course, should the required articulation of the shaftangles be limited to only one plane (e.g., only left and right, or onlyup and down), then the CV joint may be simplified, e.g., to a structuresimilar to the embodiment shown in FIG. 1.

In many trucks, the rear wheels are driven through a differential thatis located nearer the ground than is the output of the truck'stransmission, and a drive shaft incorporating our gear system can beused to provide the required articulated connection between thetransmission and the differential of such trucks. FIG. 17 is a schematicrepresentation of such a drive shaft 188 with a respective pair of ourgears 189, 190 located at each end. The internal gear 192 of gear pair189 is held in a cup-like support 193 which includes a base plate 194adapted for connection to the output of the transmission. The externalgear 195 of gear pair 189 is fixed to the left-hand end of shaft 188.Similarly, the external gear 196 of gear pair 190 is fixed to theright-hand end of shaft 188, while its mating internal gear 197 is heldin cup-like support 198 that is fixed to a shaft 199 which can beappropriately connected to the truck's differential.

Gear pairs 189, 190 on articulated shaft 188 are schematicallyrepresented as having respective ball bearings for positioning the gearsrelative to each other. Therefore, the arrangement shown in FIG. 17 isappropriate for any application in which either or both plate 194 andshaft 199 may require articulation in more than one plane. However, whenthis articulated shaft assembly is used in a truck in the manner justdescribed, the angular orientation of each gear set is usually fixed inone plane at some preselected angle and, as just indicated above,simpler gear-mounting arrangements (similar to the embodiment shown inFIG. 1) can be used for supporting the gears.

It should be noted that the total articulation provided by the geararrangement of FIG. 17 includes the maximum preferred angle of gear pair189 plus the maximum preferred angle of gear pair 190. Therefore,modifications of this arrangement can be used to provide a remarkablyarticulated joint. For instance, if the length of shaft 188 is minimized(e.g., if the two shaft ends were effectively positioned back-to-back),and if gear pairs 189, 190 were each designed to transmitconstant-velocity rotational forces under all expected loads while theshaft angles of their respective gears are varied through 30° in anyplane, then: the just-described back-to-back arrangement would provideconstant-velocity articulation up to an angle of 60° in any one plane,while providing up to 30° articulation in one plane concurrently withanother 30° articulation in any other plane.

FIG. 18 shows, schematically, a further example of an application of ourinvention as a constant-velocity joint 200 (similar to that shown inFIG. 15) incorporated in a steered drive for a vehicle. One end of asteer-drive axle 201 is splined to a conventional driving flange 202 towhich the front wheel of a vehicle is fixed by bolts (neither the wheelnor the bolts are shown). The other end of steer-drive axle 201 is fixedto a cup 204 that supports an internal gear 206 of the gear paircomprising CV-joint 200.

The external gear 207 is fixed to the end of a drive shaft 208 which, inturn, rotates in journals (not shown) held in the automotive framemember 210. Steer-drive axle 201 is suitably supported by bearings (notshown) in a wheel support 212 rotatably connected to frame member 210 bykingpins 214. The large ball bearing 216 permits the shaft angle betweengears 206, 207 to vary as wheel support 212 is steered.

Further, in other well-known conventional arrangements, e.g., in whichframe member 210 is replaced by knee-action structures for up-and-downmovement, ball bearing 216 permits concurrent articulation in thissecond plane. During such instances of concurrent articulation inmultiple planes, the gear pair 206, 207 of CV-joint 200 continues at alltimes to share two meshing areas centered 180° apart, and the gears movewith a relative nutating motion as they rotate together at a 1:1 ratio.

Attention is called to another feature of the steer-drive arrangementillustrated in FIG. 17; namely, it overcomes the torque-steer problemsthat occur in steer-drive axles with prior art CV-joints. "Torque-steer"is the term used in the art to describe the tendency of a rotating jointto create an undesirable turning moment about the kingpins of a steeredaxle. This problem is avoided in the axle design shown in FIG. 18 by thealignment of kingpins 214 with the pivot axis of CV-joint 200. Sincegears 206, 207 share two mesh points positioned 180° apart, and sincethese mesh points are aligned with the pivot axis between the drivingand driven shafts, the rotation of the gears at their 1:1 ratio createsno moment about the pivot axis; and since the pivot axis of CV-joint 200is aligned coincident with the axis of kingpins 214, the rotation of thegears creates no unwanted steering moments about the kingpin axis anddoes not result in torque-steer.

One of the important features of our constant-velocity joint relates toits ease of lubrication. FIG. 19 is a schematic and partiallycross-sectional representation of a rotating constant-velocity jointsimilar to that shown in FIG. 15. The joint is represented duringoperation as an articulated connection between two elements of an openautomotive drive shaft. At the moment illustrated, it is assumed thatthe shaft elements are articulated at an angle of about 15° and thatthey are rotating at more than 300 rpm.

An external gear 150' is mounted to a hub 152' having a circumferentialextension portion 153' splined to the end of an open drive shaft element154'. The coupling's mating internal gear 156' is mounted to a cup-likesupport 158' that includes a circumferential lip portion 159' and isfixed to the end of an open drive shaft element 160'. Attached betweencircumferential extension portion 153' of hub 152' and circumferentiallip portion 159' of cup-like support 158' is an elastomeric boot 161'.The respective ends of boot 161' are sealed against extension portion153' by a sheet metal strap 165' and against lip portion 159' by a sheetmetal collar 167'. Cup-like support 158' and elastomeric boot 161'combine to enclose the joint mechanism within an encapsulating cover.

As rotational motion is transmitted from shaft element 154' to shaftelement 160', a lubricating fluid 169' within the encapsulated joint ispressed by centrifugal forces to the sides of cup-like support 158' andinto the meshing teeth of the mating gears. Since the entire jointmechanism rotates with the axle shaft elements, the spinning metallicsides of cup-shaped support 158' are air cooled and conduct away heatgenerated in lubricating fluid 169'. Further, the vertical portions ofsheet metal collar 167' provide elastomeric boot 161' with support forrestraining the axial flow of lubricating fluid and for withstanding thepressures of this centrifuge effect.

As explained above (with reference to FIGS. 3A, 3B, and 3C), whileangularly-intersecting external gear 150' and internal gear 156' rotateat a 1:1 ratio, their mating teeth continuously slide into and out ofmesh at their two shared meshing areas positioned 180° apart. That is,as the joint shown in FIG. 19 rotates through one-quarter of arevolution, teeth 150a, 150b of external gear 150' slide across therespective faces of mating teeth 156a, 156b of internal gear 156' andinto full mesh, carrying lubrication fluid pressed against them when inthe position illustrated. After another one-quarter revolution, thesegears move out of mesh and the spaces between the teeth of the gears areagain filled with lubricating fluid pressurized by the centrifuge actionof the rotating coupling. Also during operation, this sliding motion ofthe gear teeth creates a constant mist of lubrication fluid thatsaturates the atmosphere within the encapsulated joint for lubricatingthe ball bearing mechanism.

Systems with Higher Gear Ratios

The gear system can also be used to transmit rotational forces at ratiosgreater than 1:1. However, in such arrangements, the gears no longershare two meshing areas. Instead, the gears share only one meshing areain the same manner as conventional gearing, but they still transferrotational forces while their respective shafts are varied relative toeach other throughout a predetermined range of angles as explainedabove.

FIGS. 20A and 20B are schematic representations of two views of a gearsystem for transmitting rotational forces at ratios other than 1:1(e.g., 2:1). FIG. 20A shows a top view of an internal gear 220 held by acup-like support 222 that is fixed to the end of a shaft 224. A matingexternal gear 226 is formed at the end of a shaft 228 which, in thisrepresentation, has been adjusted upward in the plane of the drawing ata maximum preferred angle x above its 180° alignment position relativeto shaft 224. Gear 226 is also shown in phantom lines after shaft 228has been adjusted downward at the same maximum preferred angle x belowits 180° alignment position relative to shaft 224. As explained indetail above, the mating teeth of gears 220, 226 remain in mesh as theshaft angle changes throughout this entire range of motion.

Since gears 220, 226 have differently-sized pitch circles, they do notrotate at the same speed relative to each other. Therefore, while theirrespective tooth faces slide past each other in the manner explainedabove in regard to 1:1 ratio gear arrangements, the teeth of the smallergear 226 must also engage in rolling contact with the teeth of thelarger gear 220. To accommodate this rolling engagement in arrangementsdesigned for ratios other than 1:1, the gear teeth are provided withinvolute profiles. As indicated above, the CT and CD tooth designs arepreferably formed with straight-sided tooth profiles, and involuteprofiles cannot be readily added to either of these designs. Thus, forratios other than 1:1, the above-described lune design is preferred forthe gear teeth.

As indicated earlier, lune teeth are only in tight mesh when the gearshafts are positioned at the preferred maximum angle; and backlashbetween the mating teeth increases steadily as the shaft angledecreases, reaching maximum backlash when the shaft angle is 180°. FIG.20B is an end view of the arrangement illustrated in FIG. 20A, omittingall elements except gears 220, 226 and showing (with exaggeratedspacing) the maximum backlash that occurs when the gears are positionedwith their respective shafts aligned at 180°.

In FIG. 21, still another arrangement of the gear system isschematically represented using only external gearing. While both gears220', 226' have external teeth, this arrangement functions in a mannersimilar to that just discussed above. Namely, the gears transmitrotational forces at ratios other than 1:1 (e.g., 2:1), and the matingteeth of the gears remain in mesh at all times as the shaft anglebetween the gears changes throughout the entire range of motiondetermined by a preselected maximum angle. Further, since gears 220',226' have differently-sized pitch circles, they do not rotate at thesame speed relative to each other and, therefore, engage in rollingcontact with each other. Again, to accommodate this rolling engagementin arrangements designed for ratios other than 1:1, the gear teeth areprovided with involute profiles, and the lune design is preferred.

Also the lune teeth of gears 220', 226' are only in tight mesh when thegear shafts are positioned at the preferred maximum angle, the backlashbetween the mating teeth increasing steadily to the maximum which isreached when the shaft angle between the gears is 180°, i.e., in therelationship shown in FIG. 21. Of course, this backlash does not createa problem for those applications in which the gears are used to transferforces primarily in one direction of rotation, and the gear system canbe used to transmit such rotational forces while the shafts of the gearsare adjusted through a wide range of angles less than 180°.

We claim:
 1. A pair of gears with meshing mating teeth for transmittingrotational forces between two elements that are each rotatable about arespective one of two axes intersecting when in one of (a) the sameplane and (b) parallel planes projected one upon the other, said gearscomprising:each said gear being fixedly attachable to a respective oneof said elements for rotation therewith; each of said gears having (i) arespective pitch surface in the form of a respective pitch sphere and(ii) a respective pitch circle that is a great circle on said respectivepitch sphere; said two respective pitch spheres and said two respectivepitch circles being in one of the positions (a) wherein said two pitchspheres are concentric and have radii which are substantially identical,and said pitch circles effectively intersect with each other at twopoints separated by 180°, and (b) wherein said two pitch spheres aredifferently sized and share a single point of tangency, and said pitchcircles are respective great circles on said differently-sized spheresso that said pitch circles intersect with each other at only said pointof tangency shared by said pitch spheres; each said mating tooth havingtwo tooth faces formed so that a central portion of a lengthwise surfaceof each tooth face, when viewed on the respective spherical pitchsurface of said mating tooth, is an arc of a circle; and when said gearsare rotating in a driving and driven relationship, said intersectingaxes can be varied throughout a continuous range of angles extendingfrom 180° to a predetermined maximum angle differing from 180°.
 2. Thegears of claim 1 wherein said predetermined maximum angle at which saidaxes variably intersect is 45°.
 3. The gears of claim 1 wherein, whensaid axes are located in said parallel planes, each gear of said gearpair has external teeth.
 4. The gears of claim 3 wherein each said toothface of each said mating tooth, when viewed in a radial center plane ofsaid tooth, is substantially an involute shape in profile.
 5. The gearsof claim 1 wherein said gear pair comprises a gear with internal teethand a gear with external teeth.
 6. The gears of claim 5 wherein eachsaid tooth face of each said mating tooth of at least a first one ofsaid gears, when viewed in a radial center plane of said first gear, issubstantially straight-sided in profile.
 7. The gears of claim 6 whereinthe straight-sided profile of said tooth face follows a radial line ofsaid first gear.
 8. The gears of claim 6 wherein the straight-sidedprofile of said tooth face is spline-shaped.
 9. The gears of claim 6wherein the straight-sided profile of said tooth face has an upperaddendum that includes tip-relief crowning.
 10. The gears of claim 1wherein said central portions of both lengthwise tooth surfaces of eachsaid mating tooth of at least a first one of said gears, when viewed onthe respective spherical pitch surface of said first gear, arerespective arcs that form the opposite sides of a first single circlehaving a diameter equivalent to a predetermined normal chordal tooththickness.
 11. The gears of claim 10 wherein:each circular-arc centralportion of each said lengthwise tooth surface of said first gear has twoaxially-extending extension portions contiguous, respectively, with eachrespective end of said central portion; and each said respectiveextension portion has an axially-extending surface which, when viewed onsaid spherical pitch surface of said first gear, is a line (a) extendingfrom said circular central portion at a respective one of two pointsoppositely disposed at respective predetermined tooth surface anglesmeasured from a radial center line of said lengthwise tooth surface and(b) extending toward a projected intersection with the axial center lineof the tooth.
 12. The gears of claim 11 wherein:when said axes arepositioned at said predetermined maximum angle and each said toothpasses through meshing engagement with a tooth of said mating gear, eachsaid respective tooth surface extension portion of said first gear is astraight line that is tangent to, and that extends beyond the radialcenter line of, the circular central portion of the mating tooth of saidsecond gear.
 13. The gears of claim 11 wherein said respectivepredetermined tooth surface angles are equal to each other.
 14. Thegears of claim 13 wherein:each said tooth surface angle is equal to saidpredetermined maximum angle at which said two axes may intersect; andwhen said axes are positioned at said predetermined maximum angle, morethan two of said mating teeth of each gear are in mesh simultaneously atone of said meshing areas shared by said mating gears.
 15. The gears ofclaim 11 wherein said surface of each said respective tooth surfaceextension portion is a line tangent to said circular central portion atone of said respective points.
 16. The gears of claim 15 wherein eachsaid respective tooth surface extension portion is a straight line. 17.The gears of claim 15 wherein each said respective tooth surfaceextension portion is a curved line having a curvature inverse to thecurvature of said circular central portion.
 18. The gears of claim 17wherein said inverse curvature is the arc of a circle having a radiusequivalent to one and one-half times said diameter of said circularcentral portion.
 19. The gears of claim 17 wherein each said matingtooth of the second gear of said gear pair has two lengthwise toothsurfaces which, when viewed on the spherical pitch surface of saidsecond gear, are arcs of a second single circle having a radiusequivalent to one and one-half times the diameter of said first singlecircle that forms said circular central portion of said mating tooth ofsaid first gear.
 20. A pair of gears with meshing mating teeth fortransmitting rotational forces between two elements that are eachrotatable about a respective one of two axes that intersect when in oneof (a) the same plane and (b) parallel planes projected one upon theother, said gears comprising:each said gear being fixedly attachable toa respective one of said elements for rotation therewith, and saidmating teeth sharing at least one meshing area; each of said gearshaving (i) a respective pitch surface in the form of a respective pitchsphere and (ii) a respective pitch circle that is a great circle on saidrespective pitch sphere; said two respective pitch spheres and said tworespective pitch circles being in one of the positions (a) wherein saidtwo pitch spheres are concentric and have radii which are substantiallyidentical, and said pitch circles effectively intersect with each otherat two points separated by 180°, and (b) wherein said two pitch spheresare differently sized and share a single point of tangency, and saidpitch circles are respective great circles on said differently-sizedspheres so that said pitch circles intersect with each other at onlysaid point of tangency shared by said pitch spheres; each said matingtooth of at least a first one of said gears having two tooth facesformed so that central portions of both lengthwise tooth surfaces ofeach said mating tooth, when viewed on the respective spherical pitchsurface of said first gear, are respective circular arcs having a firstradius; and each said mating tooth of the second gear of said gear pairhaving two tooth faces formed so that each lengthwise surface of eachtooth face, when viewed on the respective pitch sphere of said secondgear, is a circular arc having a second radius selected so that, whensaid gears are rotating in a driving and driven relationship, saidintersecting axes can be varied continuously throughout a continuousrange of angles extending from 180° to an angle differing from 180° by apredetermined maximum angle.
 21. The gears of claim 20 wherein, whensaid axes are positioned at said predetermined maximum angle, more thantwo of said mating teeth of each gear are in mesh simultaneously at oneof said meshing areas shared by said mating gears.
 22. The gears ofclaim 20 wherein:each said pitch circle is, respectively, a great circleon a respective one of said two tangent spheres; one of said tangentpitch spheres is larger than the other; said larger pitch sphere formsthe pitch surface of said first gear; said arcs forming the lengthwisetooth surfaces of each said mating tooth of said first gear areconstructed with a diameter of a circle formed on the surface of saidlarger pitch sphere and subtending an angle, measured from the center ofsaid larger pitch sphere, equal to said predetermined maximum angle; andeach said mating tooth of the second gear of said pair has twolengthwise tooth surfaces which, when viewed on the respective pitchsphere of said second gear, are also arcs of a circle having the samediameter as said circular arcs forming said lengthwise tooth surfaces ofthe teeth of said first gear.
 23. The gears of claim 20 wherein:eachlengthwise tooth surface of each said mating tooth of the first gear ofsaid pair, when viewed on said pitch sphere of said first gear, has acircular-arc central portion and two axially-extending extensionportions contiguous, respectively, with a respective end of saidcircular-arc central portion; and each respective extension portion hasan axially-extending surface which, when viewed on said respectivespherical pitch surface of said first gear, is a curved line (a) havinga curvature inverse to the curvature of said circular central portion,(b) extending from and tangent to said circular-arc central portion at arespective one of two points oppositely disposed at respectivepredetermined tooth surface angles measured from a radial center line ofsaid tooth surface, and (c) extending toward a projected intersectionwith the axial center line of the tooth.
 24. The gears of claim 23wherein:said gears have a predetermined circular pitch; saidcircular-arc central portions of each said mating tooth of the firstgear of said pair form the opposite sides of a first single circlehaving a diameter equivalent to one-half said predetermined circularpitch; and said arcs forming (i) said lengthwise surfaces of the teethof said second gear and (ii) said inverse curvature of each respectiveextension portion of each said tooth surface of said first gear are allconstructed with a radius equivalent to three-quarters of saidpredetermined circular pitch.